1

Effect of Waveform Bandwidth and Array Size onTime Reversal Processing in TWIR Radar

Paramananda Jena1, Debalina Ghosh2, and A. Vengadarajan3

1Electronics and Radar Development Establishment (LRDE), Bangalore, India, Email:pj11@iitbbs.ac.in2School of Electrical Sciences (SES), IIT, Bhubaneswar, India, Email:dghosh@iitbbs.ac.in

3Defence Research Development Organisation(DRDO), Bangalore, India

Abstract—Time Reversal (TR) processing is very effectivefor imaging applications in scatterer rich environment suchas Through-the-wall Imaging (TWI). In this paper, a typi-cal Through-the-Wall imaging scenario i.e the reflections fromthe walls are exploited to improve the image focusing usingTime Reversal (TR) techniques. After extensive MATLAB basedsimulation it was found that the proposed TR based imagereconstruction scheme outperforms the conventional processingboth in down range and cross range focusing performance. Inaddition, TR focusing performance with respect to bandwidthand array size is also compared. It was observed that wallreflection multipaths can be exploited to reduce the size of TWIRarray and to use lesser bandwidth waveform for a reasonablefocusing performance.

Index Terms—Through-the-Wall Imaging Radar (TWIR),Stepped Frequency Continuous Wave (SFCW), Time Reversal(TR), Multiple-Input-Multiple-Output (MIMO).

I. INTRODUCTION

Ultra-Wide Band (UWB) radars are popular in through-the-wall(TTW) sensing. UWB Through-the-Wall Imaging Radars(TWIR) are used for hostage rescue operation, rescue ofearth quake victims and fire fighting personnel. The primarychallenge of TTW imaging is to provide a clean image ofobjects inside a building. In addition, the size and weightof the radar should desirably be small for portability andspeedy surveillance. One way is to improve the resolutionis to increase the size of the array, but that will increasethe weight and the portability of the radar gets affected.Time Reversal (TR) is an emerging technique which exploitsthe multipath environment [1] and is promising to meet theaforementioned challenge. More numbers of multipaths betterwill be the image focusing with TR, which goes againstthe conventional wisdom. The TR improvement factor is thefunction of ratio of the coherence bandwidth of the mediumto the bandwidth of the waveform [2]. If a wideband pulse istransmitted, the pulse gets broaden up due to the multipathreflections in a scatterer rich environment. The coherencebandwidth is inversely proportional to the time spread of thetarget response. It is the function of randomness of scatteringof the medium which is often referred as random medium.However, TR signal processing is very simple technique whichexploits the degrees of freedom provided by the mulitpaths toimprove the down range focusing, cross range focusing andimproved side lobe performance. In a typical TWIR, the effect

of various length of antenna, bandwidth on TR processing isstudied. In TWIR the important resources are the waveformband width and the number of antenna elements. In SFCWmodulation, large band width provides better resolution butit takes longer time for scanning the room. Similarly, forease of portability, smaller antenna is always better.TR basedimage reconstruction techniques for TWIR radar like scattererrich environment a smaller bandwidth waveform and smallerantenna can be used to obtain reasonable image focusing.

The paper is organized in the following manner. Section IIexplains about the typical TWIR through-the-wall environmentand multipaths due to walls, roofs and floor. The theory ofTR as a matched filter is discussed in section III. Section IVcovers the Time Reversal processing. Section V presents thesimulation and interpretation of the results followed by theconclusions in section VI.

II. MULTIPATHS IN A THROUGH-THE-WALL IMAGINGRADAR

The practical TWIR radar system with closely spacedtransmit and receive array known as co-located MIMO modeof operation is shown in Fig.1. Separate transmit and receivearrays provide the adequate isolation for continuous waveoperation. As the echo signal is the superposition of reflectedecho from the targets and the reflections from the walls,roof and floor as shown in Fig. 2. There is transmit arrayconsisting of Nt number of transmitters and Nr numberof receivers, depending upon the resolution requirement andquick surveillance. However, this portable class of radars sufferfrom poor resolution both in cross range and down rangedimension. It results in defocused and blurred image. Further,small antenna leads to poor cross range resolution and speedysurveillance and long depth of surveillance puts constrainton the bandwidth of the waveform, hence poor down rangeresolution. Poor resolution causes the interference of targetsechoes and scatterers echoes. It results in defocused image,ghosts and finally position of the target gets shifted from theactual position. SFCW UWB signal is being increasingly usedfor TWIR application for ease of generation and coherentprocessing. The main intent for the introductory explanationabout TWIR is to dwell on the design issue in the context ofpractical TWIR and resultant image degradation due to bothdesign constraint and environment in which radar operates. It

11th International Radar Symposium India - 2017 (IRSI-17)

NIMHANS Convention Centre, Bangalore INDIA 1 12-16 December, 2017

2

explains about propagation of signal i.e angle of incidence,angle of refraction and multipath scattering from walls ofthe room. But for the sake of simplicity, only the multipathreflections from the walls are considered here. However, itdoes not affect the research findings.

Fig. 1. TWIR radar with multipath reflections from walls

Nt is the numbers of transmitters, Nr is the numbers ofreceivers θtxi(s) is the angle of incidence w.r.t transmitter,θrxi(s) is the angle of incidence w.r.t receiver θtxr(s) isthe angle of refraction w.r.t transmitter, θrxr(s) is the angleof refraction w.r.t receive s : numbers of scatterers, (s =1, 2, 3, ......, Nsc).

(a) (b)

Fig. 2. Multipath reflections from walls, roof, floor(a) Multipaths due to walls(b) Multipath due to floor and roof

III. TIME REVERSAL AS A MATCHED FILTER

Time reversal is similar to matched filtering used in signalprocessing. The following section explains that in the presenceof highly scattered media the expression of TR is same asmatched filter. If the signal sfr (t) is transmitted by a transmitterand received by Nr numbers of receiver.

sfr (t) = sft (t) ∗ hi(t) (1)

sTRr (t) = sfr (−t) ∗ hi(t) (2)

sTRr (t) = sft (−t) ∗ hi(−t) ∗ hi(t) (3)

sTRr (t) = sft (t) ∗Rii(t) (4)

where, sft (t) is the transmit signal,hi(t) is impulse response ofthe medium, sfr (t) is the received signal after forward probing,sTRr (t) is the received signal after Time Reversal (TR), Rii(t)

is the auto-correlation function of the room for each receiverand i = 1, 2, 3, ........., Nr.

IV. TR PROCESSING

(a) Forward Probing: (i)Transmission of signal sfr (t) fromNt transmitters and reception by Nr receivers.(ii)Energy nor-malisation of the received signals for NtNr transmit andreceive pair. Signal undergoes multipath reflections from thewalls, roofs and floor. Before retransmission in TR processenergy normalisation is done to restore the signal energy. Theenergy normalisation parameter is

Ke =1

Nrc

Nrc∑i=1

‖ sTRr (t) ‖2 (5)

where,Nrc is the number of range cells, Ke is the energynormalisation parameter.

(b) Time Reversal Transmit Signal: The received signalin forward probe is energy normalised and phase conjugatedin frequency domain which equivalent to time reversal in timedomain.

sTRt (t) = Kes

f∗r (t) (6)

(c) Time Reversal Received Signal: The TR transmit signalis multiplied with the response of the medium, which is calledmathematical time reversal. Only assumption is the mediumdoes not change or slowly change during the forward probingand time reversal processing.

sTRr (t) = Kes

f∗r (t)sfr (t) (7)

where, sTRr (t) is the time reversal signal.

(d) TR reference signal: This signal required for matchedfiltering at the target location. TR process is dynamic andthe spatio-temporal focusing takes place at the target (passivescatterer). There are various techniques used to estimate theTR time which depends on the location of the target. One ofthese techniques is the minimum entropy based method [3].Here the peak detection for forward probed image is taken togenerate the reference signal.

sfref (t) = sf (t− ttgt) (8)

sfref is the reference signal which the estimated for TRfocusing at so called t = 0 of time reversal and ttgt is thetime delay of transmitter to target and target to receiver.(e) TR Matched Filtering:

sTRfil (t) = sf∗r (t)sfref (t) (9)

sTRfil (t) is the TR focused signal.

11th International Radar Symposium India - 2017 (IRSI-17)

NIMHANS Convention Centre, Bangalore INDIA 2 12-16 December, 2017

3

V. SIMULATION AND ANALYSIS

Time Reversal (TR) processing is very effective for imagingapplications in scatterer rich environment. The TWIR radarused for the simulation is given in Table I.

TABLE ITWIR SCENARIO USED FOR SIMULATION AND ANALYSIS

Simulation Parametersparameters value parameters valueRoom size 10 m x 10 m ∆f 3 MHz

Length of array 0.2m, 0.4m, 0.8m and 1.6m Rang(max) 50mNo.s of Tx 2,4,8,16 Target 4 mNo.s of Rx 2,4,8,16 BW (1-4) GHzRng. Res. 5 cm Wall type brick

Comparison of image focusing is depicted in Fig. 3. Com-parion of TR focusing improvement for different frequenciesand different length of antennas are depicted in Fig. 4, Fig. 5and Fig. 6.

Fig. 3. TR Image Focusing in range dimension

(a) (b)

Fig. 4. Down range and cross range profile for various length of antenna(a)Down range profile at 1 GHz (b) Cross range profile at 1 GHz

A. Discussions

The down range focusing due to TR is given in table II.The down range focusing factor is in the order of 20 whichextremely useful for TWIR application. It depends on thebandwidth of the waveform and the nature of the multipathscenario of the room.

Similarly as the length of the antenna increases, the sidelobeperformance gets improved as shown in table III

(a) (b)

Fig. 5. Down range and cross range profile for various length of antenna(a)Down range profile at 1.5 GHz (b) Cross range profile at 1.5 GHz

(a) (b)

Fig. 6. Down range and cross range profile for various length of antenna(a)Down range profile at 2 GHz (b) Cross range profile at 2 GHz

TABLE IIDOWN RANGE FOCUSING FOR 1.6 M ARRAY

Down Range range focusing factorBW Focusing Factor

1 GHz 161.5 GHz 202 GHz 24

TABLE IIICROSS RANGE SIDELOBE PERFORMANCE(BW: 1 GHZ) COMPARISON TR

AND CONVENTIONAL PROCESSING

Side Lobe performancelenght of arrray Side lobe level (SLL) Improvement

0.2m 20 dB0.4m 22 dB0.8m 22 dB1.6m 24 dB

VI. CONCLUSIONS AND FUTURE WORK

It is observed that for multipath reflections from wallresults in large range spread and target image gets defocused.However, with the proposed TR based image reconstructionscheme the image gets focused. After extensive simulation, itwas found that with TR, larger the bandwidth better is thedown range focusing and longer the antenna better is thesidelobe compared to conventional processing. Wall reflec-tion multipaths aids to image focusing in TR based image

11th International Radar Symposium India - 2017 (IRSI-17)

NIMHANS Convention Centre, Bangalore INDIA 3 12-16 December, 2017

4

reconstruction scheme against the conventional wisdom. Infuture, it is planed to apply the aforementioned scheme for3D resolution improvement in the MIMO TWIR radar.

REFERENCES

[1] M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L.Thomas, and F. Wu, “Time-reversed acoustics,” Reports on progress inPhysics, vol. 63, no. 12, p. 1933, 2000.

[2] M. E. Yavuz and F. L. Teixeira, “Ultrawideband microwave sensingand imaging using time-reversal techniques: A review,” Remote Sensing,vol. 1, no. 3, pp. 466–495, 2009.

[3] X. Liu, H. Leung, and G. A. Lampropoulos, “Effect of wall parameters onultra-wideband synthetic aperture through-the-wall radar imaging,” IEEETransactions on Aerospace and Electronic Systems, vol. 48, no. 4, pp.3435–3449, 2012.

Paramananda Jena has obtained his BE degree inElectronics and Telecommunication Engg.from VeerSurendra Sai University of Technology(formerlyUCE, Burla), Odisha in the year 1998 and MEdegree in Microelectronics Systems from IISc, Ban-galore in the year 2005. Currently he is scientist atLRDE,Bangalore and pursuing his PhD in the areaof Electromagnetic Time Reversal for UWB MIMOradar at IIT Bhubaneswar since January 2013. Hisareas of interests are radar signal processing, UltraWide Band MIMO Radar and Passive multi-static

Radar. He has eighteen years of experience in radar signal processing, FPGAbased signal processor development and radar system design

Dr. Debalina Ghosh received the BE degree fromJadavpur University, Kolkata, India in 2002, and theMS degree from Syracuse University, New York, in2004, both in Electrical Engineering. She receivedthe PhD degree in Electrical Engineeringfrom Syra-cuse University, New York, in 2008. Currently sheis Assistant Professor at IIT Bhubaneswar, Odisha,India. Her research interests include UWB sensors,Under ground-object identification techniques, An-tenna design for personal and satellite communica-tions, antenna arrays, theoretical and computational

electromagnetic methods, Signal processing, front -end amplifier design forRF systems and optimization methods applied to electromagnetic problems.

Dr A. Vengadarajan obtained his BE degree inElectronics and Communication Engg.. from Mad-uarai Kamraj University in 1985. He joined DRDOin 1985 since then he is working in the area ofairborne radar. He obtained his M.tech. and PHdfrom IIT Kharagpur in 1992 and 2002 respectively.His area of interest is SAR signal processing, SpaceTime adaptive Processing(STAP).

11th International Radar Symposium India - 2017 (IRSI-17)

NIMHANS Convention Centre, Bangalore INDIA 4 12-16 December, 2017